Решебник по алгебре 9 класс Мерзляк Задание 216

 

\[\boxed{\text{216\ (216).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{2} - 2ax + a^{2} - 4 = 0;\ \ \text{\ \ }\]

\[x_{1}\ и\ x_{2}\ меньше\ 5\]

\[D = 4a^{2} - 4a^{2} + 16 = 16\]

\[x_{1} = \frac{2a + 4}{2} = a + 2\]

\[x_{2} = \frac{2a - 4}{2} = a - 2\]

\[\left\{ \begin{matrix} a + 2 < 5 \\ a - 2 < 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} a < 3 \\ a < 7 \\ \end{matrix} \right.\ \]

\(\ \)

\[Ответ:a \in ( - \infty;3)\text{.\ }\]

\[\boxed{\text{216.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[S = \frac{1}{2}a \cdot b = 30\]

\[a \cdot b = 60;\]

\[a^{2} + b^{2} = 169.\]

\[Составим\ систему\ уравнений:\]

\[\left\{ \begin{matrix} a \cdot b = 60\ \ \ \ \ \ \ \ \ \\ a^{2} + b^{2} = 169 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} a = \frac{60}{b}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \left( \frac{60}{b} \right)^{2} + b^{2} = 169 \\ \end{matrix} \right.\ \]

\[\frac{3600}{b^{2}} + b^{2} - 169 = 0\ \ \ \ | \cdot b^{2}\]

\[3600 + b^{4} - 169b^{2} = 0\]

\[b^{4} - 169b^{4} + 3600 = 0\]

\[b^{2} = x:\]

\[x^{2} - 169x + 3600 = 0\]

\[D = 28\ 561 - 14\ 400 =\]

\[= 14\ 161 = 119^{2}\]

\[x_{1} = \frac{169 + 119}{2} = \frac{288}{2} = 144;\]

\[x_{2} = \frac{169 - 119}{2} = \frac{50}{2} = 25.\]

\[b^{2} = 144\]

\[b_{1} = 12.\]

\[b^{2} = 25\]

\[b_{2} = 5.\]

\[a_{1} = \frac{60}{b} = \frac{60}{12} = 5;\]

\[a_{2} = \frac{60}{b} = \frac{60}{5} = 12.\]

\[Ответ:5\ см\ и\ 12\ см.\]